Chapter 8 – Compression
Aims:
Outline the objectives of compression.
Define the key methods used to compress data.
Outline methods used to compress images, video and audio.
Key factors in reducing the amount of data storage
• Getting rid of redundant data. This involves determining the parts
of the data that are not required
• Identifying irrelevant data. This involves identifying the parts of the
data which are perceived to be irrelevant.
• Converting the data into a different format. This will typically
involve changing the way that the data is processed and stored
• Reducing the quality of the data. Often the user does not require
the specified quality of the data.
RGB
256
240
224
208
192
176
160
144
128
112
96
80
64
48
32
16
0
#FF0000 (255,0,0)
#00FF00 (0,255,0)
#0000FF (0,0,255)
#FFFFFF (255,255,255)
#000000 (0,0,0)
#6496C8 (100,150,200)
#C89664 (200,150,100)
#64C896 (100,200,150)
Red
256
240
224
208
192
176
160
144
128
112
96
80
64
48
32
16
0
256
240
224
208
192
176
160
144
128
112
96
80
64
48
32
16
0
Green
Blue
Changes between images
(0,0)
Previous image
(4,0)
(0,16)
(4,16)
Current image
Red,
Green,
Blue
Convert
Convert
to
toDigital
Digital
MPEG-1
MPEG-1
or
orMPEG-2
MPEG-2
compression
compression
Convert
Convert
to
toDigital
Digital
MPEG
MPEGAudio
Audio
(MP-3)
(MP-3)
compression
compression
Convert
Convert
to
toDigital
Digital
WAV
file
BMP
file
JPEG/GIF
JPEG/GIF
compression
compression
Compression reduces
redundancy in the data
MPEG
movie
MP-3
sound file
JPEG/GIF
picture file
Audio, image and video compression
• JPEG/GIF. The JPEG (Joint Photographic Expert Group) compression
technique is well matched to what the human eye and the brain
perceive.
• MPEG. MPEG (Motion Picture Experts Group) uses many techniques
to reduce the size of the motion video data.
• MPEG (MP-3). The digital storage of audio allows for the data to be
compressed.
Compression process
Animation
Text
Digital
Storage/
Transmission/
Processing
Data
conversion
Compression
Data
conversion
Uncompression
1011101010
Sound
Video
Sampling
ADC
Compression/
Data conversion
Filter
DAC
Uncompression/
Data conversion
1101
Digital
Storage/
Transmission/
Processing
Sampling
Ts
sample
Quantization
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
1011
1011
1001
0111
Error and number of conversion bits
1 Full Scale
Max error   .
N
2
2
Bits (N)
Quantization
levels
Accuracy
(%)
1
2
25
2
4
12.5
3
8
4
16
Bits (N)
Quantization
levels
Accuracy
(%)
8
256
0.2
12
4096
0.012
6.25
14
16384
0.003
3.125
16
65536
0.00076
Lossy and lossless compression
•
•
Lossless compression. Where the data, once uncompressed, will be
identical to the original uncompressed data. This will obviously be the
case with computer-type data, such as data files, computer programs,
and so on, as any loss of data may cause the file to be corrupted.
Lossy compression. Where the data, once uncompressed, cannot
be fully recovered. It normally involves analysing the data and
determining which data has little effect on the perceived information.
Entropy and source coding
• Entropy coding. This does not take into account any of the
characteristics of the data and treats all the bits in the same way. As it
does not know which parts of the data can be lost, it produces
lossless coding. Typical coding techniques are:
– Statistical encoding. Analysing the occurrence and patterns of data.
– Suppressing repetitive sequences.
• Source encoding. This normally takes into account characteristics of
the information.
Entropy coding
Normally, general data compression does not take into account the type of
data which is being compressed and is lossless. As it is lossless it can be
applied to computer data files, documents, images, and so on. The two main
techniques are statistical coding and repetitive sequence suppression.
•
•
Huffman. Huffman coding uses a variable length code for each of the
elements within the data. This normally involves analysing the data to
determine the probability of its elements. The most probable elements are
coded with a few bits and the least probable coded with a greater number of
bits. This could be done on a character-by-character basis, in a text file, or
could be achieved on a byte-by-byte basis for other files.
Lempel-Ziv. Around 1977, Abraham Lempel and Jacob Ziv developed the
Lempel–Ziv class of adaptive dictionary data compression techniques (also
known as LZ-77 coding), which are now some of the most popular
compression techniques.
Huffman
Letter:
No. of occurrences:
‘e’
57
‘b’
12
‘c’
3
‘e’
57
‘i’
51
‘i’ ‘o’ ‘p’ ‘b’ ‘c’
51 33 20 12 3
‘e’ 57
‘e’ 57
‘e’ 57
68
‘i’ 51
‘i’ 51
‘i’ 57
‘e’ 57 [1]
‘o’ 33
‘o’ 33
‘p’ 20
‘p’ 20 [1]
‘b’ 12 [1]
‘c’
3 [0]
‘o’
33
15 [0]
35 [1]
108 [1]
68 [0]
‘i’ 51 [0]
‘o’ 33 [0]
‘e’
‘o’
‘b’
11 ‘i’ 10
00 ‘p’ 011
0101 ‘c’ 0100
‘p’
20
Huffman example (goals scored)
1 goal [34]
1 goal [34]
1 goal [34]
1 goal [34]
0 goals [21]
0 goals [21]
0 goals [21]
[22]
2 goals [15]
2 goals [15]
2 goals [15]
0 goals [21]
3 goals [14]
3 goals [14]
3 goals [14]
1
4 goals [5]
4 goals [5]
1
4 goals [8]
0
[3]
0
5 goals [2]
1
6 goals [1]
0
1
Coding:
0 goals
1 goal
2 goals
3 goals
4 goals
5 goals
6 goals
0
01
11
00
101
1001
10001
10000
[56]
[36]
2 goals [15]
[36]
1 goal [34]
1
1 goal [34]
[22]
0
[22]
1
0
0 goals [21]
2 goals [15]
Huffman (cont.)
11000110100100110100
will be decoded as:
‘e’ ‘o’ ‘p’ ‘c’ ‘i’ ‘p’ ‘c’
‘e’
‘o’
‘b’
11 ‘i’ 10
00 ‘p’ 011
0101 ‘c’ 0100
Lempel-Ziv
‘The receiver#9#3quires a#20#5pt for it.
This is automatically sent wh#6#2 it #30#2#47#5ved.’
LZW
The Lempel–Ziv–Welsh (LZW) algorithm (also known LZ-78) builds a
dictionary of frequently used groups of characters (or 8-bit binary values
A simple example is to use a six-character alphabet and a 16-entry dictionary,
thus the resulting code word will have 4 bits. If the transmitted message is:
ababacdcdaaaaaaef
Then the transmitter and receiver would initially add the following to its
dictionary:
0000
0010
0100
0110–1111
‘a’
‘c’
‘e’
empty
0001
0011
0101
‘b’
‘d’
‘f’
LZW (cont.)
0000
0010
0100
0110–1111
‘a’
‘c’
‘e’
empty
0001
0011
0101
‘b’
‘d’
‘f’
0000
0010
0100
0110
‘a’
‘c’
‘e’
‘ab’
0001
0011
0101
0111–1111
‘b’
‘d’
‘f’
empty
Statistical coding
• Statistical encoding is an entropy technique which identifies certain
sequences within the data. These ‘patterns’ are then coded so that
they have fewer bits. Frequently used patterns are coded with fewer
bits than less common patterns. For example, text files normally
contain many more ‘e’ characters than ‘z’ characters. Thus the ‘e’
character could be encoded with a few bits and the ‘z’ with many bits
a
00000
b
00001
c
00010
d
00011
e
00100
f
00101
g
00110
h
00111
i
01000
j
01001
k
01010
l
01011
m
01100
n
01101
o
01110
p
01111
q
10000
r
10001
s
10010
t
10011
u
10100
v
10101
w
10110
x
10111
y
11000
z
11001
SP
11010
Pure coding (example)
Morse coding
a
01
b
1000
c
1010
d
100
e
0
f
0010
g
110
h
0000
i
00
j
0111
k
101
l
0100
m
11
n
10
o
111
p
0110
q
1101
r
010
s
000
t
1
u
001
v
0001
w
011
x
1001
y
1011
z
1100
SP
0011
Repetitive character sequence suppression
• Repetitive sequence suppression involves representing long runs of a
certain bit sequence with a special character. A special bit sequence is
then used to represent that character, followed by the number of
times it appears in sequence.
8.3200000000000
could be coded as:
8.32F11
where F is a special flag.
Source compression
• Source compression takes into account the type of information that is
being compressed, and is typically used with image, video and audio
information.
For example the following might be integer values for the samples:
321, 322, 324, 324, 320, 317, 310, 311
This could be coded as difference values as:
321, +1, +2, 0, –4, –3, –7, +1
Image compression
File
Compression type
Max. resolution
or colours
TIF
F
Huffman RLE
and/or LZW
48-bit colour
TIFF (tagged image file format) is typically
used to transfer graphics from one computer
system to another. It allows high resolutions
and colours of up to 48 bits (16 bits for red,
green and blue).
GIF
LZW
65,563 65,536
(24-bit colour,
but only 256
displayable
colours)
Standardized graphics file format which can be
read by most graphics packages. It has similar
graphics characteristics to PCX files and allows
multiple images in a single file and interlaced
graphics.
JPG
JPEG compression
(DCT, quantization
and Huffman)
Depends on the
compression
Excellent compression technique which
produces lossy compression. It normally results
in much greater compression than the methods
outlined above.
Image compression
Image with
a good deal
of repetition
Image with
a good deal
of changes
Type
Size(B)
Compression (%)
BMP
308278
100.0
BMP
301584
97.8
BMP, RLE encoded
GIF
124304
40.3
GIF, Version 89a, non-interlaced
GIF
127849
41.5
GIF, Version 89a, interlaced
BMP
750054
100.0
TIF
136276
44.2
TIF, LZW compressed
BMP
7832
1.0
BMP, RLE encoded (256 colours)
TIF
81106
26.3
TIF, CCITT Group 3, MONOCHROME
PCX
31983
4.3
PCX, Version 5 (256 colours)
JPG
28271
9.2
JPEG – JFIF Complaint (Standard coding)
GIF
4585
0.6
GIF, Version 89a, non-interlaced (256 colours)
JPG
26511
8.6
JPEG – JFIF Complaint (Progressive coding)
TIF
26072
3.5
TIF, LZW compressed (16.7M colours)
JPG
15800
2.1
JPEG (Standard coding, 16.7M colours)
JPG
12600
1.7
JPEG (Progressive coding, 16.7M colours)
BMP, RBG encoded (640480, 256 colours)
Type
Size (B)
Compression (%)
BMP, RBG encoded (500500, 16.7M colours)
JPEG
• It is a compression technique for grey-scale or colour images and uses
a combination of discrete cosine transform, quantization, run-length
and Huffman coding.
The components are computed from the RGB components:
Y =
Cb =
Cr =
0.299R+0.587G+0.114B
0.1687R–0.3313G+0.5B
0.5R–0.4187G+0.0813B
 7 7
(2 y  1)v 
1
(2 x  1)u

F ( u, v )  C ( u) C ( v ) 
f ( x , y ) cos
cos
4
16
16
 x 0 y 0



1
where C ( z ) 
if z  0
2
or
1
if z  0

MPEG
Reference
Reference
frame
frame
YUV
RGB
RGBto
to
YUV
YUV
converter
converter
Images
Block
Block
matching
matching
YUV
DCT
DCT
transform
transform
Error
terms
Quantization
Quantization
DCT
terms
Run
Run
Length
Length
encoding
encoding
Quantized
DCT terms
Huffman
Huffman
coding
coding
Zero
suppressed
Variable
length code
Segmentation
352 pixels
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
288 pixels
I, P and B-frames
•
•
•
Intra frame (I-frame). An intra frame, or I-frame, is a complete image and
does not require any extra information to be added to it to make it complete.
As it is a complete frame, it cannot contain any motion estimation processing.
It is typically used as a starting point for other referenced frames, and is
usually the first frame to be sent.
Predictive frame (P-frame). The predictive frame, or P-frame, uses the
preceding I-frame as its reference and has motion estimation processing. Each
macroblock in this frame is supplied as referenced to an I-frame as either a
vector and difference, or if no match was found, as a completely encoded
macroblock (called an intracoded macroblock). The decoder must thus retain
all I-frame information to allow the P-frame to be decoded.
Bidirectional frame (B-frame). The bidirectional frame, or B-frame, is
similar to the P-frame except that it references frames to the nearest
preceding or future I- or P-frame. When compressing the data, the motion
estimation works on the future frame first, followed by the past frame. If this
does not give a good match, an average of the two frames is used. If all else
fails, the macroblock can be intracoded.
Audio compression
Digitized audio signal rate = 44.116 kbps = 705.6kbps
Sampler
ADC
Audio out
Parallelto-serial
Storage/
Transmission
Clock
Serial
bit stream
Filter
Audio out
DAC
Serialto-parallel
Phase
locked
loop (PLL)
Clock
information
Psycho-acoustic model
amplitude
Actual
audio
spectrum
masking level
frequency
amplitude
Perceived
audio
spectrum
frequency